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Chris Gilbert


Got That Perfect Bracket? Odds Are 9,223,372,036,854,775,808:1

Selection Sunday is over. You’ve got your bracket sheet. Games actually start this evening, but your office pool doesn’t start until Thursday. You are pouring over the matchups. You’re not sure how UCLA got in but you still think they can beat SMU. You know Wichita State is drooling over that second round matchup with Kansas, but can they beat Indiana? There may be money involved, or maybe it’s just bragging rights. You want your bracket to be perfect. It won’t be.

A recent article in the Chicago Tribune (mentioned in the Sacramento Bee March 5) had a DePaul University mathematics professor “crunch the numbers”. He determined the odds of predicting the correct outcome of every game in the upcoming tournament is more than 1 in 9 quintillion. That’s nine million trillion, or nine billion billion. The number is astounding. Count to a billion, then do that nine billion more times. Those are the odds. The professor pointed out that you have a better chance of winning the Powerball lottery twice in a row with two different tickets. You probably have a better chance of landing on the sun and surviving.

But, there is one flaw in the math professor’s calculation. All he did to “crunch the numbers” is multiply two by itself 63 times. In other words, those are the odds if you know nothing about basketball, and guess which team is going to win (We’re not counting the play-in games here. If we did, the odds of getting a perfect bracket are one in two-to-the-67th power, or 147,573,952,589,676,412,928:1). So if you flip a coin, the odds of it coming up heads 63 times in a row is that 1 in 9.2 quintillion number.

Let’s face it, though, Kentucky is going to beat the winner of the Hampton-Manhattan game. In 30 years of data, it’s a mathematical certainty. A one seed has never lost to a 16 seed in 120 tries. That makes the odds a little better. CBS, during its selection show Sunday, provided data for the first round matchups. A two seed is 113-7 against a 15, the three seed is 102-18 against the 14, etc. The five seed does have a winning record against the 12, but the five is more likely to lose in the first round than the sixth seed (that really mucks things up, doesn’t it). Also, you should at least pick two nine seeds when you fill out your bracket. The nine actually has the better record than the eight, going 61-59.

So now we’re not flipping coins anymore. Taking all four nine seeds, we multiply all those percentages together, then take that total and raise it to the fourth power (there are four 1-16 matchups, four 2-15s, 3-14s, etc). If my math is right (better than 1 in 9.2 quintillion it is, but no certainty of course), your odds of getting all 32 of the first round games correct is about one in 22,575. It’s still a longshot, but if you guessed on all the games, your odds are about one in 4.3 billion (4,294,967,296 or 2 to the 32nd power—two possible outcomes in 32 different games).

Those are just the odds to be perfect through Friday. After that, you are on your own. You’ve got to think that Kentucky is going to beat Purdue or Cincinnati, but if you guess the rest of the way out (31 more games, or 2 to the 31st power), multiply that by the 22-and-a-half thousand figure instead of the 4.3 billion, and your odds of a perfect 64-team bracket are now just 48,479,959,064,056:1 (1 in about 48-and-a-half billion). There, don’t you feel better? It’s still much easier to win the Powerball, but I got your odds of a perfect bracket down to the billions instead of the billions of billions. Of course, I could be wrong. Happy bracketing everyone.

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